So-called biosensors for detecting the time courses of the formation of analyte-ligand complexes are known in a wide variety of embodiments, and other apparatuses, for example including array systems, are also usable for detecting such reactions. What are detected are both the time courses of the association of the analyte on the ligand when the analyte concentration is increased by adding an analyte solution of a specific concentration, as well as the dissociation upon addition of a lower-concentration solution or one of zero concentration. In general, the time course of complexation is described using the function R(t) or Rt, the concentration of the complex or its change over time being referred to as ct(LA) or dct(LA)/dt. To a first approximation, a first-order exponential curve is assumed for the time course of function R, with exponent kon upon association and koff upon dissociation of the complex. It has hitherto been usual, for detection of these values, to measure the reaction, e.g. the complexation, partially, or until attainment of an equilibrium value Req at which association of the analyte+ligand complex is in equilibrium with its dissociation. Dissociation of the complex, and a regeneration and washing phase, then follow. This is a very time-consuming process, especially when multiple measurements with different concentration changes need to be performed successively. A further evaluation of the exponents that have been obtained yields the actual kinetic rate constants of interest, but the method requires a constant analyte concentration.
In existing methods for evaluating the measured values, it is usually assumed that the concentration of the analyte added to the ligand is constant, despite complexation. This is approximated, for example, by having the analyte concentration be many times greater than the ligand concentration, or by continuous exchange in the flowthrough system. In actuality, however, a depletion of the analyte or a concentration change always occurs, for example, in the context of association in the cuvette system, with the result that the equilibrium value R′eq that is actually attained differs from the hypothetical value Req at a constant analyte concentration. Although analysis of the measured values with a second-order approximation function yields a more accurate value for the coefficient of the exponential function, it is nevertheless complicated and requires additional determination or consideration of a number of experimental boundary conditions.
Initial rates are employed for concentration determination. The initial rates are obtained by placing a compensation line at the beginning of the association curve; its slope underestimates the initial rate, however, since the straight line does not take into account the curvature of the curve. It is also known that when plotting the initial rates on a diagram against the analyte concentration c(A), in a context of multiple measurements with different concentrations each time, in theory a straight line through the origin, with slope Rmax*kass, is obtained, Rmax being the maximum possible reaction e.g. of the biosensor to addition of an excess of an analyte. The slope of this straight line is, however, also distorted by the underestimate mentioned above, so that this type of diagram is not employed for determining kass.
The measured values are detected using, inter alia, biosensors on the flowthrough principle or cuvette principle, a very wide variety of measurement methods being known in the existing art. In flowthrough systems, a sensor surface on which the ligand is immobilized is impinged upon, for each analysis, by a constant flow of an analyte solution. The approximation of a preselected constant analyte concentration is applied here. In cuvette systems, a measurement cell is filled with an analyte solution and the reaction with the ligand on a sensor surface is detected. Distortion of the measurement results occurs here in particular, since actual reactions cause the analyte concentration to change. When multiple measurement operations with different concentrations are being performed in succession, normally the cuvette is purged with a buffer solution or otherwise regenerated, and then a solution with a different concentration is introduced.
In the context of multiple titrations, i.e. changes in concentration, the measurement curves have hitherto been recorded until complexation has reached an equilibrium state. Only the equilibrium states are used for the determination of further variables, but not of the kinetics or initial rates. Access to the kinetics is in fact explicitly ruled out with multiple-step titrations of this kind.
For flowthrough systems, so-called sample loops arranged sequentially behind one another, which are filled successively and can be purged out into the measurement chamber, are known. The sample loops each have, however, a volume that is exactly defined in a manner that is laborious in terms of production engineering, and between them an undefined extra volume also called the “dead volume.” Undesirable mixing of different solutions can occur in the dead volume. The loops cannot be filled from their outlet side, or partially, or even independently of one another; and they cannot be purged into the measurement chamber independently of one another.